Various optical spectroscopic measurement systems have been developed for the noninvasive monitoring of blood constituent concentrations. In such systems, light of multiple wavelengths is used to illuminate a thin tissue portion of a person, such as a fingertip or earlobe, to obtain a spectrum analysis of the light absorbed by blood flowing through the tissue site. Pulse oximetry systems, which perform such measurements to monitor blood oxygenation of hemoglobin constituents, have been particularly successful in becoming the standard of care. Extending this technology to the noninvasive monitoring of other blood constituents, such as blood glucose, is highly desirable. For example, current methods for accurately measuring blood glucose involve drawing blood from the subject, which can be onerous for diabetics who must take frequent samples to closely monitor blood glucose levels.
FIG. 1 illustrates an optical spectroscopic measurement system 100. A multiple wavelength light source 110 produces incident light 112 of intensity I0 and wavelength xcex, I0,xcex, which illuminates a sample 120 having multiple constituents, each of concentration ci. The incident light 112 is partially absorbed by the sample 120, and transmitted light 130 of intensity I emerges from the sample 120. A detector 140 provides an output signal 142 that is proportional to the transmitted light 130. A signal processor 150 operates on the detector output signal 142 to provide a measurement 152 that is indicative of one or more of the constituent concentrations ci in the sample 120, based upon the known extinction coefficients xcex5i,xcex of the sample constituents.
The attenuation of light through a homogenous, non-scattering medium of thickness d having n dissolved, absorbing constituents is described by the Beer-Lambert Law                     I        ⁢                  xe2x80x83                =                  xe2x80x83                ⁢                              I                          0              ,                              xe2x80x83                            ⁢              λ                                ⁢                      xe2x80x83                    ⁢                      ⅇ                          -                                                ∑                                      i                    ⁢                                          xe2x80x83                                        =                                          xe2x80x83                                        ⁢                    1                                    n                                ⁢                                  xe2x80x83                                ⁢                                                      ϵ                                          i                      ,                                              xe2x80x83                                            ⁢                      λ                                                        ·                                      c                    i                                    ·                  d                                                                                        (        1        )            
Dividing both sides by I0,xcex and taking the logarithm yields
ln(I/I0)=xe2x88x92xcexcaxc2x7dxe2x80x83xe2x80x83(2a)
                              μ          a                =                              ∑                          i              =              1                        n                    ⁢                                    ϵ                              i                ,                λ                                      ·                          c              i                                                          (2b)            
where xcexca is the bulk absorption coefficient and represents the probability of absorption per unit length. Measurements are taken at n wavelengths to yield n equations in n unknowns                               [                                                                      ln                  ⁡                                      (                                                                  I                                                  λ                          1                                                                                            I                                                  0                          ,                                                      λ                            1                                                                                                                )                                                                                                                        ln                  ⁡                                      (                                                                  I                                                  λ                          2                                                                                            I                                                  0                          ,                                                      λ                            2                                                                                                                )                                                                                                      ⋮                                                                                      ln                  ⁡                                      (                                                                  I                                                  λ                          n                                                                                            I                                                  0                          ,                                                      λ                            n                                                                                                                )                                                                                ]                =                              -                                          [                                                                                                    ϵ                                                  1                          ,                                                      λ                            1                                                                                                                                                              ϵ                                                  2                          ,                                                      λ                            1                                                                                                                                      ⋯                                                                                      ϵ                                                  n                          ,                                                      λ                            1                                                                                                                                                                                                  ϵ                                                  1                          ,                                                      λ                            2                                                                                                                                                              ϵ                                                  2                          ,                                                      λ                            2                                                                                                                                      ⋯                                                                                      ϵ                                                  n                          ,                                                      λ                            2                                                                                                                                                                          ⋮                                                              ⋮                                                              ⋰                                                              ⋮                                                                                                                          ϵ                                                  1                          ,                                                      λ                            n                                                                                                                                                              ϵ                                                  2                          ,                                                      λ                            n                                                                                                                                      ⋯                                                                                      ϵ                                                  n                          ,                                                      λ                            n                                                                                                                                              ]                            ⁡                              [                                                                                                    c                        1                                                                                                                                                c                        2                                                                                                                        ⋮                                                                                                                          c                        n                                                                                            ]                                              ⁢          d                                    (        3        )            
which can be written in matrix notation as
I=xe2x88x92A(xcex)Cdxe2x80x83xe2x80x83(4)
Solving for the constituent concentrations yields                     C        =                              -                          1              d                                ⁢                                    A              ⁡                              (                λ                )                                                    -              1                                ⁢          I                                    (        5        )            
If the medium is a tissue portion of a person, such as a fingertip, it includes a number of constituents that absorb light. Some of the principal absorbing constituents in tissue include water, oxyhemoglobin, reduced hemoglobin, lipids, melanin and bilirubin. A drawback to applying the Beer-Lambert Law to determine the concentrations of absorbing constituents, however, is that tissue is a turbid media, i.e. strongly scatters light, which violates an underlying assumption of equation (1). Scattering in tissue is due, in part, to the variations in refractive index at the boundaries of cells or other enclosed particles, such as collagen fibers, mitochondria, ribosomes, fat globules, glycogen and secretory globules.
FIG. 2 illustrates a particular photon path 200 as it travels through a turbid medium 202. The photon path 200 is shown as a series of connected vectors {right arrow over (p)}li each representing the direction and pathlength of a particular photon between collisions. The total pathlength traveled by the photon is                     pl        =                              ∑                          i              =              1                        n                    ⁢                                                    pl                ix                2                            +                              pl                iy                2                            +                              pl                iz                2                                                                        (        6        )            
As shown in FIG. 2, the effect of scattering is to substantially increase the photon pathlength and, hence, the probability of absorption. Thus, when a turbid media is considered, the Beer-Lambert Law is modified to include the effective pathlength, pl, which is a function of wavelength. The Beer-Lambert Law is also written in terms of transmission, T, to differentiate reflected light due to back-scattering of the incident light.                     T        =                              T            max                    ⁢                      ⅇ                          -                                                ∑                                      i                    =                    1                                    n                                ⁢                                                      ϵ                                          i                      ,                      λ                                                        ·                                      c                    i                                    ·                                      pl                    λ                                                                                                          (        7        )            
where Tmax is the maximum transmitted light without absorption.                               [                                                                      ln                  ⁡                                      (                                                                  T                                                  λ                          1                                                                                            T                                                  max                          ,                                                      λ                            1                                                                                                                )                                                                                                                        ln                  ⁡                                      (                                                                  T                                                  λ                          2                                                                                            T                                                  max                          ,                                                      λ                            2                                                                                                                )                                                                                                      ⋮                                                                                      ln                  ⁡                                      (                                                                  T                                                  λ                          n                                                                                            T                                                  max                          ,                                                      λ                            n                                                                                                                )                                                                                ]                =                  -                                                    [                                                                                                    pl                                                  λ                          1                                                                                                            0                                                              0                                                              0                                                                                                  0                                                                                      pl                                                  λ                          2                                                                                                            0                                                              0                                                                                                  0                                                              0                                                              ⋰                                                              0                                                                                                  0                                                              0                                                              0                                                                                      pl                                                  λ                          n                                                                                                                    ]                            ⁡                              [                                                                                                    ϵ                                                  1                          ,                                                      λ                            1                                                                                                                                                              ϵ                                                  2                          ,                                                      λ                            1                                                                                                                                      ⋯                                                                                      ϵ                                                  n                          ,                                                      λ                            1                                                                                                                                                                                                  ϵ                                                  1                          ,                                                      λ                            2                                                                                                                                                              ϵ                                                  2                          ,                                                      λ                            2                                                                                                                                      ⋯                                                                                      ϵ                                                  n                          ,                                                      λ                            2                                                                                                                                                                          ⋮                                                              ⋮                                                              ⋰                                                              ⋮                                                                                                                          ϵ                                                  1                          ,                                                      λ                            n                                                                                                                                                              ϵ                                                  2                          ,                                                      λ                            n                                                                                                                                      ⋯                                                                                      ϵ                                                  n                          ,                                                      λ                            n                                                                                                                                              ]                                      ⁡                          [                                                                                          c                      1                                                                                                                                  c                      2                                                                                                            ⋮                                                                                                              c                      n                                                                                  ]                                                          (        8        )            xe2x80x83T=xe2x88x92X(xcex)A(xcex)Cxe2x80x83xe2x80x83(9)
C=xe2x88x92A(xcex)xe2x88x921X(xcex)xe2x88x921Txe2x80x83xe2x80x83(10)
FIG. 3 illustrates one method of measuring the effective pathlength through a sample. A picosecond pulse laser 310 and an ultra-fast detector 340 directly measure the photon xe2x80x9ctime of flightxe2x80x9d through a sample 320. A single pulse 360 with a duration on the order of a picosecond is directed through the sample 320. The detector 340 measures the corresponding impulse response 370. The time difference between the light entering the sample 312 and the mean time of flight, {overscore (t)}380, of light having traversed the sample 330 yields the mean optical pathlength, i.e. the effective pathlength
mpl=cv{overscore (t)}/nsxe2x80x83xe2x80x83(11a)
                              t          _                =                              ∫            0            ∞                    ⁢                                    T              ⁡                              (                t                )                                      ⁢            t            ⁢                          xe2x80x83                        ⁢                                          ⅆ                t                            /                                                ∫                  0                  ∞                                ⁢                                                      T                    ⁡                                          (                      t                      )                                                        ⁢                                      xe2x80x83                                    ⁢                                      ⅆ                    t                                                                                                          (11b)            
where cv is the speed of light in a vacuum and ns is the refractive index of the sample.
An analytic expression for the shape of the impulse response of a narrow collimated pulsed light beam normally incident on the surface of a semi-infinite homogeneous tissue slab of thickness d, derived from the diffusion approximation to radiative transfer theory, is
                                          T            ⁡                          (                              d                ,                t                            )                                =                                                    (                                  4                  ⁢                  π                  ⁢                                      xe2x80x83                                    ⁢                  Dc                                )                                            -                                  1                  2                                                      ⁢                          t                              -                                  3                  2                                                      ⁢                          e                              -                                  μ                  a                  ct                                                      ⁢                          f              ⁡                              (                t                )                                                    ⁢                  xe2x80x83                ⁢                  
                                    (                  12a                )                                          f          ⁡                      (            t            )                          =                  {                                                    (                                  d                  -                                      z                    0                                                  )                            ⁢                              e                                  -                                      [                                                                                            (                                                      d                            -                                                          z                              0                                                                                )                                                2                                                                    4                        ⁢                        Dct                                                              ]                                                                        -                                          (                                  d                  +                                      z                    0                                                  )                            ⁢                              e                                  -                                      [                                                                                            (                                                      d                            +                                                          z                              0                                                                                )                                                2                                                                    4                        ⁢                        Dct                                                              ]                                                                        +                                          (                                                      3                    ⁢                    d                                    -                                      z                    0                                                  )                            ⁢                              e                                  -                                      [                                                                                            (                                                                                    3                              ⁢                              d                                                        -                                                          z                              0                                                                                )                                                2                                                                    4                        ⁢                        Dct                                                              ]                                                                        -                                          (                                                      3                    ⁢                    d                                    +                                      z                    0                                                  )                            ⁢                              e                                  -                                      [                                                                                            (                                                                                    3                              ⁢                              d                                                        +                                                          z                              0                                                                                )                                                2                                                                    4                        ⁢                        Dct                                                              ]                                                                                }                                    (                  12b                )            xe2x80x83D={3[xcexca+(1xe2x88x92g)xcexcs]}xe2x88x921xe2x80x83xe2x80x83(12c)
z0=[(1xe2x88x92g)xcexcs]xe2x88x921xe2x80x83xe2x80x83(12d)
where T(d, t) is the spatially integrated transmittance, D is the diffusion coefficient, c is the speed of light in the tissue, xcexca is the bulk absorption coefficient, xcexcs is the bulk scattering coefficient and g is the anisotropy, which is the mean cosine of the scattering angle. Equations (12a)-(12d), therefore, are an approximation of the impulse response 370 shown in FIG. 3. The derivation of equations (12a)-(12d) and a description of the model upon which that derivation is based, is given in Time Resolved Reflectance and Transmittance for the Noninvasive Measurement of Tissue Optical Properties, Patterson et al., Applied Optics, Vol. 28, No. 12, Jun. 15, 1989, Optical Society of America, incorporated in its entirety by reference herein. The Patterson article also provides an expression for the mean pathlength                     mpl        ⁢                  xe2x80x83                =                  xe2x80x83                ⁢                                                            (                                  4                  ⁢                                      xe2x80x83                                    ⁢                                                            xe2x80x83                                        ⁢                                          μ                      a                                                        ⁢                                      xe2x80x83                                    ⁢                  D                                )                            ⁢                              xe2x80x83                                                    -                              1                2                                              ⁢                      xe2x80x83                    ⁢                                                                      (                                      d                    ⁢                                          xe2x80x83                                        -                                          xe2x80x83                                        ⁢                                          z                      0                                                        )                                ⁢                                  xe2x80x83                                ⁢                                  ⅇ                                      (                                          2                      ⁢                                              xe2x80x83                                            ⁢                                                                        xe2x80x83                                                ⁢                                                  z                          0                                                                    ⁢                                              xe2x80x83                                            ⁢                                                                                                    μ                            a                                                    /                          D                                                                                      )                                                              ⁢                              xe2x80x83                            -                              xe2x80x83                            ⁢                              (                                  d                  ⁢                                      xe2x80x83                                    +                                      xe2x80x83                                    ⁢                                      z                    0                                                  )                                                                    ⅇ                                  (                                      2                    ⁢                                          xe2x80x83                                        ⁢                                                                  xe2x80x83                                            ⁢                                              z                        0                                                              ⁢                                          xe2x80x83                                        ⁢                                                                                            μ                          a                                                /                        D                                                                              )                                            ⁢                              xe2x80x83                            -                              xe2x80x83                            ⁢              1                                                          (        13        )            
As equation (13) indicates, the mean pathlength is dependent on geometry and the concentration of various blood constituents and dynamically changes in tissue as the geometry and blood concentration changes. A way of dynamically determining the mean pathlength through a tissue sample is needed in order to reasonably estimate constituents such as blood glucose. Unfortunately, a measurement system such as described with respect to FIG. 3, above, is both large and expensive, confining its use to optical laboratories rather than clinical use. Instead, the pathlength measurement system of the present invention estimates the mean pathlength by measuring the magnetically-induced optical rotation of polarized light as it passes through a tissue sample.
One aspect of the present invention is a physiological monitor for measuring a blood constituent concentration within a tissue portion of a subject. The monitor has a polarized light source adapted to illuminate the tissue portion with an incident light beam and a magnetic field generator configured to impose a magnetic field on the tissue portion while illuminated by the light source. The magnetic field imparts a rotation in the plane of polarization of the incident light beam as it propagates through the tissue portion and emerges as a transmitted light beam. The monitor also has a polarimeter with an input responsive to the transmitted light beam and an output corresponding to the rotation. The monitor further has a signal processor in communications with the polarimeter output so as to compute an output corresponding to a mean pathlength estimate of the tissue portion. In one embodiment of the physiological monitor, the polarized light source and the polarimeter are adapted to provide spectroscopic measurements of the tissue portion, and the signal processor combines those spectroscopic measurements with corresponding mean pathlength estimates to provide an output indicative of the blood constituent concentration. In another embodiment of the physiological monitor, a separate spectrometer provides the spectroscopic measurements of the tissue portion and the signal processor provides corresponding mean pathlength estimates that are combined with the spectroscopic measurements to indicate the blood constituent concentration.
In yet another embodiment of the physiological monitor described in the above paragraph, the magnetic field generator alternately imposes a plurality of magnetic fields on the tissue portion. A first one of the fields encodes with a first rotation those photons traveling through the sample generally on-axis with the light beam. A second one of the fields encodes with a second rotation those photons traveling through the sample generally off-axis with the light beam. The mean pathlength measurement is a function of the second rotation relative to the first rotation. In a particular embodiment, the first one of the fields is a uniform field coaxial with the incident light beam and the second one of the fields is a uniform field orthogonal to the first one of the fields. In another particular embodiment, the first one of the fields is a uniform field coaxial with the incident light beam and the second one of said fields is a non-uniform field coaxial with the incident light beam. In yet another particular embodiment, the mean pathlength measurement is a ratio of the second rotation to the first rotation. In a further embodiment of the physiological monitor, the magnetic field generator alternately imposes a plurality of orthogonal magnetic fields on the tissue portion and the mean pathlength estimate is a function of a corresponding plurality of rotations in the plane of polarization of the incident light beam imparted by the fields. In a particular embodiment, the function is proportional to a square-root of a sum of the squares of the rotations.
Another aspect of the present invention is a physiological monitor for measuring a blood constituent concentration within a tissue portion of a subject having a light source adapted to illuminate the tissue portion with a monochromatic light polarized in a first direction and a magnetic field generator configured to alternately impose a first magnetic field and a second magnetic field on the tissue portion while illuminated by the light. The first field imparts a first rotation on the light and the second field imparts a second rotation on the light. The monitor also has a detector responsive to light intensity polarized in a second direction. The detector provides a first output corresponding to the first rotation and a second output corresponding to the second rotation so as to compensate for scattering in the tissue portion when calculating a blood constituent concentration. In one embodiment, the magnetic field generator is a Helmholtz coil configured to generate a first uniform magnetic field coaxially to the light source and a second uniform magnetic field orthogonally to the first uniform magnetic field. In another embodiment, the magnetic field generator is a pair of generally planar permanent magnets. The magnets are fixedly mounted parallel to each other and are rotatable between a first position that generates a first uniform magnetic field coaxially to the light source and a second position that generates a second uniform magnetic field orthogonally to the first uniform magnetic field. In yet another embodiment, the magnetic field generator is a pair of generally planar permanent magnets. The magnets are each hinged to move between a first position parallel to each other so as to generate a first uniform magnetic field coaxially to the light source and a second position tilted towards each other so as to generate a second non-uniform magnetic field coaxial to the light source.
A further aspect of the present invention is a physiological monitoring method for measuring a blood constituent concentration within a tissue portion of a subject. The method comprises the steps of illuminating the tissue portion with a polarized light beam, applying a magnetic field to the tissue portion, measuring a rotation in polarization of the light beam after transmission through said tissue portion, estimating a mean photon pathlength from the rotation and applying the mean pathlength to a spectroscopic measurement to determine the constituent concentration. In one embodiment, the method also comprises the steps of measuring an attenuation of light transmitted through the tissue portion and estimating an absorption from the result of the measuring. The applying step has the substeps of combining the mean photon pathlength and the absorption to compute a constituent concentration. In another embodiment, the method also has the steps of applying a second magnetic field to the tissue portion, measuring a second rotation in polarization of the light beam after transmission through the tissue portion, and calculating a ratio of the rotation and the second rotation so as to estimate a mean path length.
Yet another aspect of the present invention is a physiological monitor for measuring a blood constituent concentration within a tissue portion of a subject. The monitor comprises a light source means for illuminating the tissue portion with a polarized light beam and a generator means for imparting a rotation of the polarized light beam as it propagates through the tissue portion. The monitor also comprises a detector means for outputting a measure of the rotation and a processor means for utilizing the measure to provide a compensation for scattering within the tissue portion. In one embodiment, the monitor further comprises a spectroscopic measurement means for providing an estimate of a blood constituent concentration within the tissue portion and a compensation means for combining the compensation with the estimate to improve the estimate.